u"r is equivalent to u"r"_ when r<0.
<@(>"_1) i. 3 4
+---------+
|0 1 2 3|
|4 5 6 7|
|8 9 10 11|
+---------+
<@(>"1) i. 3 4
+-------+-------+---------+
|0 1 2 3|4 5 6 7|8 9 10 11|
+-------+-------+---------+
<@:(>"1) i. 3 4
+---------+
|0 1 2 3|
|4 5 6 7|
|8 9 10 11|
+---------+
Whether >"r is the proper inverse for <"r is a question I don't have an
answer for.
Henry Rich
On 11/9/2021 3:28 PM, Jan-Pieter Jacobs wrote:
Recently, I was playing around with inverted tables, specifically (from
https://code.jsoftware.com/wiki/Essays/Inverted_Table):
ifa =: <@(>"1)@|: NB. inverted from atoms
afi =: |:@:(<"_1@>) NB. atoms from inverted
x0=: ];._1 ' Smith Jones Chan Wilson Saxon Angelo Smith Wilson'
x1=: ];._1 ' John Dakota Wilson Diana Joan Roberto John John'
x2=: 0 1 0 1 1 0 0 1
x3=: 23 29 47 23 31 19 23 23
x4=: 1.25 0.97 2.11 1.25 2.8 1.11 1.25 1.25
x=: x0;x1;x2;x3;x4
It occured to me both operations afi and ifa are (or should be) actually
inverses of each other, but was baffled to find for once J did not work as
expected:
afi b. _1
<@(>"_1)@:|:
ifa
<@(>"1)@|:
x -: ifa afi x
1
x -: afi inv afi x
|domain error
| x-: afi inv afi x
<@(>"1) |: afi x
┌──────┬───────┬───────────────┬───────────────────────┬──────────────────────────────────────┐
│Smith │John │0 1 0 1 1 0 0 1│23 29 47 23 31 19 23 23│1.25 0.97 2.11 1.25
2.8 1.11 1.25 1.25│
│Jones │Dakota │ │ │ │
│Chan │Wilson │ │ │ │
│Wilson│Diana │ │ │ │
│Saxon │Joan │ │ │ │
│Angelo│Roberto│ │ │ │
│Smith │John │ │ │ │
│Wilson│John │ │ │ │
└──────┴───────┴───────────────┴───────────────────────┴──────────────────────────────────────┘
<@(>"_1) |: afi x
|domain error
| <@(>"_1)|:afi x
|: afi x
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│Smith │Jones │Chan │Wilson │Saxon │Angelo │Smith │Wilson │
├───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│John │Dakota │Wilson │Diana │Joan │Roberto│John │John │
├───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│0 │1 │0 │1 │1 │0 │0 │1 │
├───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│23 │29 │47 │23 │31 │19 │23 │23 │
├───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│1.25 │0.97 │2.11 │1.25 │2.8 │1.11 │1.25 │1.25 │
└───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
As far as I understood, >"_1 and >"1 on a rank 2 array should be identical,
shouldn't they?
Apparently dissect also chokes on this sentence, as well as the "correct"
one:
load 'debug/dissect'
dissect '<@(>"_1) |: afi x' NB. problematic sentence
assertion failure
|assertion failure: traversedowncalcselect
| ((*/frame)>#selx)+.(*/frame)=#selx['travdowncalcselect'
Error during initial display
dissect '<@(>"1) |: afi x'
error in paint
domain error
|domain error: cd
| glrect 0 0 1 1+"1^:(-.IFQT),"2|."1 y
If not for these oddities, it looks like the inverses of afi and ifa would
be correctly derived by J, as I expected:
afi
|:@:(<"_1@>)
ifa b. _1
|:@(<"1@>)
ifa
<@(>"1)@|:
afi b. _1
<@(>"_1)@:|:
I'm curious what your take is on this.
Best regards,
Jan-Pieter
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